Simplify the following expression: $n = \dfrac{2t^2 + 26t + 72}{t + 4} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $2$ , so we can rewrite the expression: $ n =\dfrac{2(t^2 + 13t + 36)}{t + 4} $ Then we factor the remaining polynomial: $t^2 + {13}t + {36} $ ${4} + {9} = {13}$ ${4} \times {9} = {36}$ $ (t + {4}) (t + {9}) $ This gives us a factored expression: $\dfrac{2(t + {4}) (t + {9})}{t + 4}$ We can divide the numerator and denominator by $(t - 4)$ on condition that $t \neq -4$ Therefore $n = 2(t + 9); t \neq -4$